Dozens of South Korean bank and credit-card executives offered to resign Monday over the theft of personal information belonging to more than 100 million cardholders.

The executives at KB Financial Group, NongHyup Financial Group and Lotte Group sought to take responsibility for the breach after a single engineer whose firm, Korea Credit Bureau, was hired by all three financial companies, allegedly stole the sensitive information. Phone numbers, email and home addresses and card numbers were among the data stolen.

At KB Financial, 27 executives handed in their resignations, which the company chairman will decide whether or not to accept, according to The Wall Street Journal. NongHyup accepted the resignation of Sohn Kyoung-ik, the head of its credit-card unit. Nine Lotte executives offered to resign. Their resignations await approval by the company's board of directors.

Data breaches are becoming increasingly common and larger in scale, raising questions about the wisdom of entrusting one's financial well-being to banking institutions and credit-card companies whose security is lacking.

Sometimes personal and financial data is leaked from another source. Target and Neiman Marcus were both hacked late last year, spilling customer information into the hands of criminals.

By contrast to the South Korean executives, however, Target chief Gregg Steinhafel, has not offered to resign -- nor has the public pressured him to -- following the massive data breach, which leaked the credit card numbers and other personal information of some 110 million customers.

"I know that it is frustrating for our guests to learn that this information was taken and we are truly sorry they are having to endure this," Steinhafel said in a statement. "I also want our guests to know that understanding and sharing the facts related to this incident is important to me and the entire Target team."

On Jan. 13, Steinhafel appeared on CNBC to apologize again, and said Target would cover any fraudulent charges related to the breach and would even provide affected customers with free credit monitoring for up to one year. Target plans to "work really hard to become an even better retailer over time," Steinhafel added.

Should Target's top executives resign over the massive data breach, or have they taken sufficient action? Tell us in the comments below.